I think this says "Buchou made the customer refund "me" ("me" sounding like the object being refunded in this case, as if you're a currency.) I may be wrong here, though. With one verb, and three to four objects being affected or doing something in this scenario, I get rather confused as to which particle to use. On an unrelated note, however, I think お客さん would be more appropriate. Especially since you're attaching the honorific お、 leaving off さん sounds odd.

I let the dog eat.
僕は犬に食べさせる。

Nothing wrong really, but this sounds more like "I will(future tense) let the dog eat."

Bill ate my daifuku!
僕の大福はビルさんに食べられた。

Again, nothing wrong here, but a better English translation would be "My daifuku was eaten by bill"

She is said to be beautiful.
彼女は美しいと言われた。

This sounds to me like "She was told she is beautiful." Perhaps a better way of wording this would be "彼女は美しいと言われる"

Do you have past tense and present/future mixed up?

電車は東京駅で止まらせられます。
This means "The train will be made to stop at tokyo station"

For past tense, change ます to ました。 Also, I think 東京駅に would be more appropriate than 東京駅で here. I may be wrong, but in this context, で makes it sound like the train just happened to be told to stop while it was at tokyo station. に makes tokyo station the target, or destination of stopping.

If I have any of this wrong, I trust that someone else will come and correct me as also. I'm still not sure how to properly word the first sentence.

Hah, I don't. I did happen to write those examples up along with my translations of them around 1:00 AM when my caffeine powered buzz was wearing off. Anyway, thanks for pointing those out, I didn't even to bother proofreading those the next day.

As far as the use of で, in:
電車は東京駅で止まらせられます。
I figure since it refers to where the event happens, で works just fine.

I'm also not sure about the first sentence, that を particle has been bugging me.

Once again, the use of passives with inanimate objects is unusual. The passive is used *much* more commonly in English than it is in Japanese. I suggest that you read a more detailed explanation of the passive in Japanese rather than just trying to translate English passive sentences into Japanese.